The π-hydrogen bonded minimum on the standard and the counterpoise-corrected B3LYP, PBE1PBE/6-31++G(d,p) and MP2/6-31++G(d,p) potential energy hypersurfaces of the methanol–fluorobenzene dimer is studied. Anharmonic OH stretching frequency shift calculated at MP2 level is in excellent agreement with the experiment (20.5 vs. 20 cm −1), while all DFT values are too large, the B3LYP results being superior to the PBE1PBE ones, especially for the counterpoise-corrected PES. The OH stretching vibrational potentials are analyzed with the charge field perturbation methodology. Interaction and dissociation energy calculations, along with the NBO and AIM analyses of the MP2 and Kohn–Sham densities are carried out as well.